Three identical rods $A, B$ and $C$ are placed end to end. $A$ temperature difference is maintained between the free ends of $A$ and $C$. The thermal conductivity of $B$ is thrice that of $C$ and half of that of $A$. The effective thermal conductivity of the system will be ($K_{A}$ is the thermal conductivity of rod $A$).

The dimensions of thermal resistance are

$A$ composite metal bar of uniform cross-section is made up of a length of $25 \ cm$ of copper,$10 \ cm$ of nickel,and $15 \ cm$ of aluminium. Each part is in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at $100^{\circ}C$ and the aluminium end at $0^{\circ}C$. The whole rod is covered with an insulating belt so that no heat loss occurs at the sides. If $K_{\text{Cu}} = 2K_{\text{Al}}$ and $K_{\text{Al}} = 3K_{\text{Ni}}$,what will be the temperatures of the $\text{Cu-Ni}$ and $\text{Ni-Al}$ junctions,respectively?

Two rods whose lengths are $l_1$ and $l_2$ with thermal conductivity coefficients $k_1$ and $k_2$ are placed end to end. The thermal conductivity coefficient of a uniform rod of length $l_1+l_2$ whose thermal resistance is the same as that of the system of these two rods is

Two metal plates of equal thickness have thermal conductivities $K_1$ and $K_2$ respectively. They are joined together to form a single plate. The equivalent thermal conductivity of this composite plate is ..........

Two rods $A$ and $B$ of different materials but same cross-section are joined as shown in the figure. The free end of $A$ is maintained at $100^{\circ}C$ and the free end of $B$ is maintained at $0^{\circ}C$. If $l_2 = 2l_1$,$K_1 = 2K_2$ and the rods are thermally insulated from the sides to prevent heat losses,then the temperature $\theta$ of the junction of the two rods is ........ $^{\circ}C$.